ABOUT INVESTIGATION OF SYSTEMS WITH FIRST INTEGRALS
          L.A. Bourlakova, V.D. Irtegov
    (Institute of Systems Dynamics and Control Theory SB RAS
        134, Lermontov St., Irkutsk, 664033, Russia
            E-mail : irteg@icc.ru )

The report discusses three examples of using computer algebra in
investigation of mechanical systems.
1. Obtaining first integrals.
The subject of discussion are the cases (i) when the system of differential
equations has simplest groups of symmetry, (ii) when we need to
determine parameters of the system from existence conditions of the
first integral of specific form.
2. Obtaining partial solutions of the system of differential equations
with first integrals. Here we find existence conditions of stationary
motions and discuss variants of their solvability.
3. Investigation of stability of stationary motions.  We provide
examples from dynamics of single rigid body and system of rigid bodies.

Keywords: computer algebra, first integrals, stationary solutions, stability.